WP 11/30

Survival expectations, subjective health and smoking:evidence from European countries

Silvia Balia

September 2011

york.ac.uk/res/herc/hedgwp

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Survival expectations, subjective health and smoking:

evidence from European countries.

Silvia Balia*

Università di Cagliari

September, 2011

1 Abstract

This work aims to assess risk perception of smokers in reporting survival expectations and

subjective health. In particular, the analysis investigates individuals’ perception of smoking

effects in the short and long-term and whether they believe that such detrimental effects can

be reversed. Data from the Survey of Health, Ageing and Retirement in Europe, which

contain a numerical measure of subjective survival probability, are used to estimate a

simultaneous recursive system of equations for survival expectation, subjective health and

smoking. Endogeneity and unobservable heterogeneity are addressed using a finite mixture

model. This approach identifies two types of individuals that differ in level of optimism, risk

perception and rationality in addiction. One important result is that for both types past

smokers perceive smoking consequences as reversible, with some difference between the

short and long-term. We also find evidence of differences among current and past smokers in

the way they evaluate the opportunity cost of tobacco consumption.

Keywords: survival expectations; subjective health; risk; smoking; EM algorithm.

JEL codes I12, C0, C30, C41.

* CRENoS, Università di Cagliari, viale S. Ignazio, 78, 09123, Cagliari, Italia. E-mail

address: silvia.balia@unica.it

Acknowledgments

The author wishes to thank Andrew Jones, Casey Queen, Teresa Bago d’Uva, Martin Forster, Rinaldo Brau,

Silvana Robone, Cinzia Di Novi and participants at the SIEP conference (2008) and at iHEA congress in

Toronto (2011) for their suggestions and comments.

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2 Introduction

In the last decade many European countries have been committed in tobacco control action

plans and smoke-free legislation. Nevertheless, the failure to fully account for individual

perception of the consequences of current and past smoking can likely reduce the impact of

policy interventions. This motivates studying smoking behaviour and risk perception of

smokers.

Measures of beliefs about survival probability can be used in models of health investments

to investigate choices of unhealthy behaviours, such as smoking, over the life cycle.1

Researchers need to be aware, however, that such measures might be largely affected by

individual perception of risk, which depend on how individuals evaluate the costs and benefits

associated with their behaviour. In particular, the empirical literature has provided mixed

evidence on the role of smoking on perception of health and mortality risks as well as on

heterogeneity in how perceived risk is related to smoking status (Gerking and Khaddaria,

2011). Viscusi (1990) support the idea that both smokers and non smokers overestimate the

contribution of smoking to the onset of lung cancer. In contrast, Schoenbaum (1997) finds

that heavy smokers (defined by number of cigarettes smoked) tend to underestimate the

negative effect of smoking intensity on survival probability. Studying how smokers perceive

their own mortality risk in response to smoking-related and general health shocks, Smith et al.

(2001a, 2001b) find a significant difference between categories of smokers. Heavy smokers

are more optimistic about future survival than they should be; current smokers reduce their

survival expectations more dramatically than former and never smokers when they experience

smoking-related health shocks. Khwaja (2007) find that, when reporting survival

expectations, current smokers are very optimistic while past smokers are relatively

pessimistic.

The economic literature explains smoking behaviour according to two alternative theories,

which may be of help to understand risk perception of smokers. One theory defines smokers

as myopic individuals who care more about present satisfaction than about the future (see

Thaler and Sheffrin, 1981; Winston, 1980): tobacco consumption is a commodity that

enhances instantaneous utility and its negative effects on future health and risk of dying are

not taken into account. According to the theory of rational addiction, smokers are forward-

1 Beliefs about future events are crucial to understand how individuals make economic decisions.

Income and return expectations elicited from survey questionnaires, for example, have largely been

used in models of consumption and saving (see, Guiso et al.,1992).

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looking individuals who take into account future consequences of their decisions (Becker and

Murphy, 1988), meaning that the detrimental effects of smoking are internalised. Thus,

forward-looking smokers decide to smoke only if the benefits outweigh the costs of smoking,

and present-oriented (myopic) individuals are potentially more addicted.

More recent works have reconciled these views. Carbone et al. (2005) define a theoretical

model based on expected lifetime utility and describes how rational individuals might change

their smoking behaviour depending on different perceptions of the health effects. Arcidiacono

et al. (2007) investigate whether models of forward-looking behaviour explain heavy smoking

(and drinking) better than models of myopic behaviour in the elderly, taking into account

unobservable heterogeneity. Assuming that the myopic model can be simply nested within the

forward-looking model, they show that both models predict decreasing smoking rates:

smoking is less attractive as individuals age, when more illnesses occur and health worsens.

Sharp declines are predicted by the fully rational model, where, however, individuals aged 50-

62 years old smoke more than myopic individuals; after the age of 62 and up to the age of 80,

smoking rates are higher in the myopic model; at that cut-off age of 80 there is an upward

trend in smoking behaviour. This “end-of-life effect” is what Becker and Murphy would

defined as a rationally myopic attitude of older people, the latter being less concerned with

future effects on health. The relationship between the dynamics in smoking behaviour and age

is confirmed also in other studies: Orphanides and Zervos (1995) and Kremers et al. (2004)

find that the youngsters, typically subject to strong peer influences, are more likely to

experiment with smoking. In addition to that, for them there is still a perception of long

lifespan during which they can compensate for smoking effects by diversifying their

investments in health.

This work aims to assess risk perception of smokers in reporting survival expectations and

subjective health. In particular, our analysis will try to understand whether individuals believe

that the effects of smoking are reversible. Reversibility would imply, for example, an

understatement of the true effect of time spent smoking as long as smokers quit at some point

in their life.2 This is of particular concern in the case anti-tobacco campaigns pass the

information that smoking is bad for your health but that quitting cancels out long-term risks.

Specifically, using information on duration of the smoking habit, our analysis investigates

individual perception of smoking effects in the short-term, that is on current health status (for

2 Using numerical simulation, Carbone et al. (2005) compare two hypothetical and extreme scenarios

where individual’s beliefs about the probability of death depend on health and past smoking (the

irreversible case) and on health only (the reversible case).

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example smoking might have effects on pulse rate, blood pression, weight), as well as in the

long-term, that is on mortality risk (this is expected to be higher for smokers since the risk of

onset of lung cancer or cardiovascular diseases, for example, is higher compared to the non-

smoking population).

This study adds to the empirical literature on risky health behaviours in a number of ways.

First, it specifies a simultaneous recursive model for individual survival expectations,

subjective health and smoking behaviour that accounts for unobservable factors (such as

genetics, individual rates of time preference, level of risk aversion and optimism, ability to

internalise available information about health and longevity risks) that might simultaneously

affect them. This is possible thanks to the estimation of a finite mixture model, via the EM

algorithm, that allows identifying two homogenous individual classes in the population and

class membership probabilities. Second, the empirical analysis makes use of data on elderly

Europeans whilst most of the evidence on risk perception of smokers is based on US data.

Third, smoking behaviour is measured as the number of years spent smoking which gives us

the scope for analysis of the hazard of quitting. This enables us to shed new light on

differences among types of smokers, and across classes, in reporting survival expectations and

health. One important result is that in both classes past smokers perceive smoking

consequences as reversible, with some difference between the short and long-term. Such

attitudes in risk perception are interpretable, particularly for older smokers, in terms of

myopic behaviour. Our results combines alternative ways of explaining smoking behaviour:

one that tries to understand how individuals perceive the health consequences of smoking and

others that are based on the traditional approach that emphasises utility maximisation of

rational individuals (see Cawley and Ruhm, 2011). Finally, our analysis also shows that

numerical indicators of subjective survival probability are complete measures of survival

expectations that could be used in models of health investments over the life-cycle.

3 Data and variables

We use data from the first wave (2004) of the the Survey of Health, Ageing and

Retirement in Europe (SHARE), a survey designed after the role models of the HRS and the

English Longitudinal Study of Ageing (ELSA).3 The target population of the survey consists

of non-institutionalised individuals, and their spouses, aged 50 or older. The SHARE provides

3This paper uses data from SHARE release 2.4.0 supplied by the CentERdata. SHARE data collection

in 2004-2007 was primarily funded by the European Commission through its 5th and 6th framework

programmes. More information are available http://www.share-pro ject.org/.

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rich information about health and lifestyles as well as survival expectations, which has so far

been absent from European surveys. The original sample is made of 31,115 individuals, with

a response rate of about 85 per cent. For the purpose of our analysis and because of item non

response, this has been reduced to 20,524 respondents aged 50 to 85 years old, from northern

(Denmark and Sweden), central (Austria, Belgium, Germany, France and the Netherlands)

and southern Europe (Italy, Spain and Greece).

3.1 Indicator of survival expectations

Survival expectations are measured by a numerical indicator of subjective survival

probability (SSP). This is derived from the question “What are the chances that you will live

to be age T or more?”. The distribution of SSP is approximated by proposing a different target

age (T) to each individual depending on her age class. We consider target ages of 75, 80, 85,

90 and 95, where the distance from current age is between 14 and 25 years (see Table 1). We

exclude individuals older than 85 years old, because of low frequency in the sample, as well

as those who were not matched to the appropriate target age.

TABLE 1

The question on SSP is the ninth of eleven questions about predicted probabilities of future

events. Responses are driven by a card reporting a sequence of numbers from 0 (“absolutely

no chance”) to 100 (“absolutely certain”). A warm-up question, “What do you think the

chances are that it will be sunny tomorrow?”, is asked to help respondents feel at ease with

probabilities. Nevertheless, we excluded records with unreliable responses according to a

criterion based on two questions about the chance that the standard living will be better and

worse. A subjective probability of 0 for both events indicates a high expected probability that

the standard living will be unchanged. If the probabilities sum to greater than 1, this would

indicate that subjective assessment of future events is unreliable.4

Eliciting survival expectations through predicted probabilities is usually preferred to asking

qualitative questions: probabilities permits a better comparison across individuals, while

qualitative responses may depend on cognitive, linguistic and cultural differences and usually

suffer from response bias. Furthermore, internal consistency of probabilities can be assessed

(Juster, 1966; Dominitz and Manski, 1997; Manski, 2004). The main disadvantage of using

using SSP, however, is heaping at focal values such as 0, 50, 100 an values ending with a

zero. Figure 1 shows the distribution of SSP at each target age and for each European region

4 We use a tolerance level of 0.10 and exclude only individuals for whom the sum of the probabilities

is higher than 1.10.

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considered. Around 4.1 per cent of all respondents report to have no chance to survive to the

target age, 25.2 per cent report a SSP of 50 and 15.8 per cent are certain to survive. Responses

are more concentrated at higher values, as 60, 70, 70 and 90. We deal with this issue in the

econometric modelling by choosing an appropriate parametric distribution for SSP.

Another advantage of using a quantitative measure of expectations is that the distribution

of SSP is comparable with either probabilities computed from life tables or observed

mortality. Life tables are usually found to understate survival probability and SSP is broadly

considered a better predictor of future mortality than objective life table hazard rates.5 A

comparison of SSP from the SHARE to actuarial survival probabilities from life tables, by

Peracchi and Perotti (2010), confirm this view and show that life tables omit important

individual characteristics while subjective probabilities may be affected by the individual’s

level of optimism. Figure 1 also shows compares average SSP with average probabilities of

survival calculated from period life tables for 2004, available in the Human Mortality

Database. As expected, average SSP decreases with target age. Southern Europeans report, on

average, higher probabilities than the others, except for survival at 75 where Northern

Europeans are more optimistic (SSP is 72 per cent). SSP at 75, 80 and 85 are always lower

that those calculated from life tables; the opposite is true for survival at 90 and 95. This might

capture the fact that SSP likely depends upon observable (socioeconomic status, health and

risk factors) as well as unobservable individual characteristics influencing beliefs (such as

level of optimism), which are not included in life tables.

FIGURE 1

3.2 Measures of subjective health and smoking behaviour

A commonly used measure of general health status is self-assessed health (SAH) (see

Deaton and Paxson, 1998; Smith, 1999): it measures perceived health but is known to be a

good indicator of morbidity and a powerful predictor of future health and mortality (Idler and

Benyamini, 1997; van Doorslaer and Gerdtham, 2003). Respondents are asked “How is your

health?” and can answer “excellent”, “very good”, “good”, “fair”, “poor”. We use a

5 Hurd and McGarry (1995) show that SSP is internally consistent if compared to the average survival

probability from life tables and covaries well with socio-economic variables and risk factors as actual

mortality does. Hurd et al. (1999) and Hurd and McGarry (2002) stress the role of unobservable

heterogeneity in SSP, whereas life tables only capture the effect of demographic factors on mortality.

Despite being correlated with health and the onset of diseases, SSP is not simply an alternative

measure of overall health status: it has an element of expectations that accounts for most of the

unobservable heterogeneity, understanding which would help in the estimation of life-cycle models.

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dichotomised version of SAH that takes the value 1 if health is excellent or very good, and 0

otherwise.6

The SHARE also provides rich information about tobacco smoking habit. On the basis of

the questions, “Have you ever smoked cigarettes, cigars, cigarillos or a pipe daily for a period

of at least one year?”, “Do you smoke at the present time?”, it is possible to know whether

respondents never smoked, are current smokers or have quit by the time of the interview (past

smokers). Combining this information to responses at the question “How old were you when

you stopped smoking?” we build a duration time variable, indicating the number of years

spent smoking. This variable is right-censored at the time of the interview for current smokers

who can eventually quit; complete spells of smoking are observed only for past smokers.

3.3 Descriptive statistics

Table 2 reports sample means for the variable used to describe the sample. Average SSP is

61.9 per cent; 32 per cent of respondents are in excellent or very good health. Current

smokers counts for 20 per cent of the sample and have already smoked for 36.5 years on

average. About 28.6 per cent of smokers have quit by the time of the interview and have

smoked for 22.5 years.

Table 2 also compares individuals whose SSP is equal to 50 per cent with those who report

lower and higher probabilities. A 50 per cent SSP might reflect “epistemic uncertainty” rather

than probabilistic thinking (Bruine de Bruin et al., 2002). This should not preclude, however,

the possibility that such response is a genuine survival expectation (Hill et al., 2005). The

proportion of respondents in excellent or very good health increases monotonically moving

from the group with SSP lower than 50 to the group with the highest SSP. The same trend is

found in the number of disabilities. The proportion of sedentary and obese individuals

decreases moving from the group with lower to that with higher SSP; while the proportion of

drinkers and smokers increases. Current smokers, however, are more concentrated in the 50

and higher SSP groups, while past smokers in the highest probability group. As expected,

longer smoking duration are associated with lower probability. Individuals in poor socio-

economic status are concentrated in the group with lower SSP. For those who report a SSP

lower than 50 more mothers, fathers and spouses have already died with respect to the other

two groups, where the age at death of parents is , in fact, slightly higher. On the contrary,

higher SSP is associated with lower age at death of the spouse. Overall, observable

6 Etilè and Milcent (2006) find that a way to reduce reporting heterogeneity in SAH is to convert the

ordered variable in a binary variable.

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differences across subgroups suggests that a 50 per cent SSP is likely to be a genuine

response.

TABLE 2

3.4 Variation with health, smoking, socioeconomic variables and parental mortality

Observed variation in SSP should be in line with epidemiological evidence on the relation

between mortality risk, health status, smoking and socioeconomic status. Table 3 shows that,

survival expectations get dramatically lower moving from excellent to poor health and

decrease as individuals age (that is, for higher target ages). Surprisingly, average SSP at ages

75, 80 and 85 is higher for past relative to current and never smokers, while the lowest

probabilities is reported by current smokers; average SSP at age 90 is higher for current and

never smokers. If we look at the overall distribution, past and current smokers report the

highest average SSP. As expected, SSP is positively related to income and education.

TABLE 3

Table 4 shows that the first and second quartiles of the SSP distribution are mainly

composed by individuals in good and fair health; the second quartile also includes a larger

proportion of individuals in very good health. The last two quartiles show larger variation in

the distribution of SAH and include fewer individuals in fair health. Never smokers, however,

represent about half of individuals in each SSP quartile and this proportion decreases

monotonically moving from the first to the last quartile. The composition of each SAH

category by smoking status is very alike. Never smokers are more concentrated in the fair

category, past smokers in the excellent, very good and poor categories, and current smokers

are evenly spread in the five categories. Smoking durations is longer in the first and second

SSP quartile, and increases moving from the excellent to the poor health group.

TABLE 4

Other studies found a relation between parents’ death and SSP (Hurd and McGarry, 1995,

2002). With some exception, average SSP is always 10 per cent lower if one of the parents is

dead by the time of the survey (Table 5). The relation between age at death of parents and

SSP is less clear. One explanation is that parents’ early deaths are not related to children’s

survival but depend, in turn, on accidents. SSP is also higher if the spouse is still alive or died

within her fifties, declines for death between ages 51 and 74, and reaches the lowest level

when death occurs at the oldest ages.

TABLE 5

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4 Methods

Our empirical model is based on the idea of health investments, as in Grossman (1972),

and further assumes that expected lifetime utility of a rational individual depends on the

instantaneous utility derived by her own health, consumption of tobacco and other

commodities; utility is discounted by intertemporal preferences and beliefs about survival, as

in Carbone et al. (2005).

This takes the form of a simultaneous recursive model for survival expectations (sEi),

subjective health status (sHi) and smoking behaviour (Si); where sEi at any specific age

depends on sHi. The equation for sEi considers that, assessing survival, individuals weigh up

the direct effects of smoking on mortality risk as well as the indirect effects through health

(long-term effects of smoking) and is written as:

Subjective health depends on objective health (Hi), is influenced by perception of the direct

effects of smoking on current health (short-term effects of smoking), and is expressed by the

following health production function:

Smoking behaviour is defined as:

The three processes also depend on individual observable characteristics (Xi) and

unobserved factors . Health and smoking can be endogenous to survival expectations and, in

turn, smoking can be endogenous to health. This might be due to unobserved factors which

simultaneously affect formation of expectations, reporting health and smoking behaviour such

as genetics, individual rates of time preference, level of risk aversion and optimism, ability to

internalise available information about health and longevity risks.

4.1 Model specification

We approximate the distribution of SSP using the beta distribution, often employed for

proportions or subjective beliefs about probabilities of future events (Ferrari and Cribari-Neto,

2004; Smithson and Verkuilen, 2006), because it models well continuous and bounded

variables characterised by spikes at certain response foci:

(1)

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where is rescaled SSP, Γ is the gamma distribution, and ω and τ are shape parameters. 7

Maximum likelihood (ML) estimation techniques can be used.8 The expected value of SSP is

approximated by a logistic:

where, for simplicity of notation, x1

includes subjective health, smoking, socioeconomic and demographic variables.9

Other controls used to explain survival expectations are parental and spouse mortality,

which have been largely employed in previous works (see, for example, Hurd and McGarry,

2002). To control for systematic differences in reporting expectations and since respondents

are not asked to evaluate chances of survival for the same number of years (as shown in Table

1) x1 also includes age classes corresponding to target ages as well as a continuous indicator

of the difference between individual age and target age. Given the very nature of SSP, an

indicator of numeracy that captures cognitive ability is included as well.

For subjective health we use a probit model which describes the probability of being in

good or very good health:

(2)

where is SAH, is an indicator of sign and x2 are individual

characteristics including smoking, socioeconomic and demographic variables. Other controls

used to better identify the causal relation between SAH and SSP are indicators of objective

health such as disability (limitations in usual activities because of health problems, gali; in

activities of daily living, adl; in instrumental activities of daily living, iadl) and hospital

admission in the last twelve months. It is reasonable to think that these indicators have a

direct effect on reporting health but do not affect directly beliefs about survival, since

individuals usually adapt quickly to long-term disability and sudden health changes.

Smoking is modelled using a two-part specification of the duration model, which implies

splitting the sample according to starting (Douglas and Hariharan, 1994):10

(3)

7 We rescale y1 to lie in the (0, 1) interval. To avoid the logarithm of zeros and ones, y = 100 (N − 1) +

a , where N is the sample size and a is some constant (here a = 0.5). Alternative transformations can

be used. 8 One common approach is to convert the dependent variable using the logistic transformation and

then use the normal distribution for estimation. Paolino (2001) shows that ML estimation using the

beta distribution may provide more accurate and more precise results than OLS. This requires

reparametrising the likelihood function such that a location and a precision sub-model are defined. 9 Smoking indicators are two dummy variable for current and past smokers and their interactions with

smoking duration. The logarithm transformation is used to ensure flexibility. 10

Other applications can be found in Douglas (1998), Forster and Jones (2001) and Balia and Jones

(2011).

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where t is the duration of smoking, s is a binary indicator that takes value 1 if the

individual eventually started smoking, q is a binary indicator that takes value 1 if the

individual quit.11

A probit for the probability to start, describes the

first part of the model; x3 includes only income, education and demographic variables, as they

are assumed to reflect past socioeconomic characteristics influencing starting. The second part

models the hazard of quitting; it follows a Weibull distribution, with density

and survival .

12 Here is the duration

dependence parameter and is a function of covariates , where x4 includes

socioeconomic and demographic variables. 13

To better identify the causal effect of smoking

on subjective health and survival expectations indicators of drinking, physical exercise and

obesity are included. Sedentary behaviour, alcohol consumption and dietary habits are strictly

correlated with smoking behaviour (Marcus et al., 1999; Di Novi, 2010). An indicator of

smoking-related diseases diagnosed before the interview and an indicator of household

composition (the number of children) are also included. These variables might influence

directly the hazard of quitting, with only indirect effect on SAH and SSP.

Taking together equations (1) to (3), the sample likelihood of our recursive model is:

(4)

In the presence of unobservable heterogeneity ( , omitted for simplicity of notation, this

is analytically intractable and an appropriate estimation approach is needed.

4.2 Estimation approach

We propose a finite mixture model, which divides the population in a finite number of

individual types or latent classes from which the observed data come from (McLachlan and

Peel, 2000). Response variables are assumed to be independent of one another given class

membership of each individual. If this holds, a single response per individual is sufficient to

identify the model with cross-sectional data. Finite mixture models have been recently used in

11 This distinguishes between never ( ; is not observed), past ( and ) and current

smokers ( and ). 12

The Weibull is the most appropriate parametrisation for the hazard of quitting smoking (see

Douglas, 1998). In this application, it has been chosen among other distributions on the basis of

information criteria (AIC and BIC) and Cox- Snell residuals test. 13 λ is non-negative because the model is parameterised in the accelerated failure time metric.

Estimated coefficients are to be interpreted in the terms of acceleration (or deceleration) of time to

quitting.

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applications to cross-sectional data with count (see e.g., Deb and Trivedi, 1997, 2002, 2006)

and binary (see e.g., Atella et al., 2004) responses.

ML estimation of the mixture for equation (4) is achieved using the EM algorithm, usually

appropriate in the presence of incomplete or missing data (Dempster et al., 1977). Using

general notation, equation (4) can be written as where

and fk is a density function parameterised by . The expression

above assumes that there are K component densities mixed together; each pk is a mixing

proportion and can be interpreted as the prior probability ( and ) that

a data point is randomly drawn from component k. The unconditional sample log-likelihood

for the incomplete data is difficult to maximize because it contains the logarithm of a sum,

and unknown mixing parameters:

(5)

Using Bayes’ rule, we specify the posterior probability of class membership,

conditioned on covariates and the outcomes:

(6)

The estimated unconditional probability from equation (5) is the mean of the

conditional probability

. After manipulation and substituting pk

in equation (5) with its value derived from equation (6), the conditional log-likelihood is:

(7)

Estimates for are obtained by

and so the values

of maximise both the unconditional and the conditional likelihood. Intractability of the log-

likelihood is overcome because the function to be maximised has again an additive form.

The EM iterates two steps until convergence. The E-step computes the conditional

expectation of the expression and according to equation (6). The M-step

is simply implemented as the ML estimation of weighted models, using the posterior

probabilities as weights. The two steps alternate in a loop that starts with initial values for the

parameters ( ,

. At the first iteration (r) the E-step calculates

. The M-step provides the updating formulas

and

that are used to compute

. The likelihood

increases monotonically at each iteration. Under suitable regularity conditions, the sequence

13

converges to a stationary point of L(θ).14

Properties of convergence, including these

conditions, are discussed in Dempster et al. (1977), McLachlan and Krishnan (1996) and

Schafer (1997).

The number of latent classes (K) is usually chosen according to information criteria.

Typically two or three classes are chosen. We present results from a model with two classes:

this seems to provide a natural representation of our data given that it helps distinguishing

between subgroups of more and less optimistic individuals.

5 Results

Table 6 shows that, according to information criteria, such as the AIC, BIC and CAIC the

mixture model with two latent classes performs better than the single class model, thus

providing evidence of unobservable heterogeneity. The estimated parameters p1 = 0.66 and p2

= 0.34 are the probabilities that an observation is randomly drawn from the first and the

second latent class. Slope parameters are allowed to vary across classes and for each equation,

as reported in Table 7.

TABLE 6

5.1 Survival expectations

Estimated beta regression coefficients can be transformed in odds ratios (see Table 8): this

makes it possible to interpret percentage changes from the average SSP of the baseline

individual.15

This is defined as a single female aged between 81 and 85, at average distance

from target age, comes from a southern European country, is in good or less than good health,

never smoked, has low income and no education, is unemployed (or a housekeeper), her

parents are still alive, and has average cognitive ability. In class 1 the baseline individual

expects to have a 75.4 per cent probability of survival at age 95. The same baseline individual

has lower probability, 47.5 per cent, in the second latent class, thus suggesting that the two

types of individuals are characterised by a different level of optimism. As expected, average

SSP decreases in both classes when the distance between age and target age increases and is

14 The likelihood of a mixture model might not be unimodal, meaning that there are several local

maxima and a unique global maximum. The solution found by the EM loop can depend critically upon

the set of initial values for the prior probabilities and the θs. One possibility is to run the loop several

times with different initialisations and choose the best model comparing the likelihood values. Initial

values can be guessed, or can be computed as a linear transformation of the parameter estimates from

the single component model. 15

This calculation only requires exponentiating the coefficients. The odds ratio is preferred to average

partial effects because the latter measure a percentage point change, while here we want to measure a

percentage change.

14

higher in each younger age class: in particular, in class 1 average SSP is 21.5 per cent higher

for those who evaluate survival at age 90; 148 and 112 per cent higher for those who evaluate

survival at age 75 and 85 respectively. This is amplified for individuals in the second latent

class, where average SSP is 331 and 221 per cent higher for those who evaluate survival at

age 75 and 85.

TABLE 7 – 8

The role of socioeconomic variables varies across latent classes. In class 1, individuals

who belong to the second poorest income quartile expect lower SSP (-3 per cent), while those

in the highest income quartile expect higher SSP (+6 per cent) relative to the baseline. In class

2, the effect of income seems more important: being in the third (near rich) quartile implies an

increase of 13 per cent in baseline SSP. Education matters only in class 1: qualifications lower

than diploma decrease average SSP of 8 per cent. Employed individuals expect to live longer:

average SSP is 26.5 per cent higher in class 2 and 10 per cent in the first one. In class 2 also

retirement positively affect expectations (+9 per cent). In class 1, average SSP increases of

about 7 per cent for either married or separated individuals; in class 2, the contribution of

marriage is substantial and close to that of SAH (+41 per cent). Also widows expect higher

SSP (+ 27 per cent) but there is no effect of age at death of the spouse. Average SSP is

significantly associated to father’s mortality: it decreases of about 13 per cent if father died. In

class 1, however, it increases significantly for ages at death older than 50. Mather’s mortality

matters only in class 1 where average SSP is 10 per cent lower if the mother died, but

increases of about 4 per cent for ages at death higher than 80. The indicator of numeracy is

statistically significant only in class 2, where average SSP is 5 per cent higher as cognitive

ability increases. Regional dummies have a significant and larger effect in class 2, where

average SSP decreases of 23 and 28 per cent if individuals come from northern and central

Europe respectively (12 and 10 per cent in class 1).

As expected, we find that SAH explains most of the observed variation in SSP. Its effect is

predominant in class 2, where being in excellent or very good health increases average SSP of

about 54 per cent (about 37.6 per cent in class 1).

In class 1, average SSP significantly increases for past smokers (+16.6 per cent) and

quitting compensates about 4 years of smoking. This counterintuitive result can be interpreted

in terms of myopic behaviour: those who quit do not internalised the negative effect of past

smoking on mortality risk, rather they reward themselves for quitting with better chances of

living longer than their smoking behaviour would warrant. This suggest that long-term effects

are perceived as reversible. Surprisingly, indicators of current smoking habit are not

15

significant, although the signs of the coefficients show that, relative to never smokers, current

smokers expect to live shorter. In class 2, none of the smoking indicators is statistically

significant and both past and current smokers expect a slightly higher survival for an

additional year of smoking (1.3 and 0.8 per cent respectively). Overall, our results suggests

that when smoking matters (in class 1), there is still a substantial difference between current

and past smokers. Current smoking does not significantly affect formation of survival

expectation, past smoking duration has some negative effect on future mortality risk but this

is balanced out by quitting.

5.2 Subjective health

We estimate average partial effects (APE) of covariates on the probability of reporting

good or excellent health.16

Table 8 shows that the likelihood of reporting better health is

higher for individuals in the richest income quartile and for those who are employed; APEs of

these variables are bigger in the second latent class. In both classes the more educated report

better health, but having a diploma and a university or higher degree has a bigger effect in the

first latent class. In class 2 marital status is important: married, widows and separated or

divorced report better health than singletons. The probability of reporting good health

decreases with age: in class 1 it is significantly higher only for the youngest old (+5.8 per

cent), while in class 2 it is about 10 per cent higher for individuals aged 50-65 and 6 per cent

for those aged 66-70. Disability indicators have the expected effect: the probability of

reporting better health decreases with the number of limitations. Adl and iadl have a larger

impact in class 2 (+14 and 7 per cent); gali in class 1 (-30 per cent). Those who have been

hospitalised in the last year tend to report worse health: this effect is larger in class 2. Region

of origin matters more for class 2, where the probability of reporting better health is 21 and 3

per cent higher for the northern and central Europeans.

Smoking does not have a significant effect on SAH in class 1, while in class 2 the

probability of reporting better health is significantly higher for past smokers (7.7 per cent

higher than never smokers) and decreases of about 2.9 per cent for one additional year spent

smoking. This can be interpreted again in terms of myopic behaviour and reversibility.

Indicators of current smoking are not significant and the APEs are very close to that of past

smoking. These results suggest that smoking affects subjective health only in the

16 Partial effects are computed for each individual as the change in the probability that SAH equals 1

when a covariate changes, then averaged across the whole sample, so that they refer to the entire

population. We use the finite difference method for dummy variables and the calculus method for

continuous variables as in Wooldridge (2002).

16

subpopulation of the second type (the same for which smoking does not affect expected

survival). They also confirm a substantial difference between types of smokers.

5.3 Smoking behaviour

As shown in Table 7, the propensity to become a smoker is higher for men, more educated

individuals as well as for those from the youngest age cohorts in both classes. Income is

positively related to starting but the gradient of the relationship is not clear. Our model

reflects heterogeneity in the hazard of quitting. Smoking duration is predicted to be

significantly shorter for richer, retired and employed smokers, particularly in class 1.

Educated individuals smoke longer relative to those without education, particularly in class 2.

In both classes smokers with a unhealthy lifestyle, in terms of drinking and exercise, tend to

quit later, while those who have a bad dietary habit quit earlier. Northern and central

Europeans are predicted to quit earlier. The two classes differ, instead, in the way tobacco-

related diseases affect quitting: only in class 1 smokers who report diseases tend to quit

earlier. Married individuals are predicted to quit earlier than others, especially in the second

latent class. The predicted probability of starting is lower in class 1 (0.47; 0.51 in class 2),

while the estimated average smoking duration does not differ much between classes (40.8 and

40.6 years).

5.4 Predicted survival expectations and subjective health for types of smokers

Table 9 shows that predicted average SSP is higher in class 2 (65.2 per cent, 58.1 per cent

in class 1). However, predicted average probability of SAH=1 is very alike across classes

(32.2 and 32.6 per cent). We would have expected to find, instead, better health in the class

with higher expectations.

TABLE 9

The table also compares, for each latent class, predicted survival expectations and

subjective health calculated for the overall sample and hypothetical scenarios, defined on the

basis of smoking behaviour and target age. This makes it possible to discuss differences in

risk perception between never, former and current smokers. The first two columns of Table 10

show that predicted average SSP is always higher in class 2; the highest expectation (61 and

66 per cent) is associated to the scenario where all individuals quit smoking. In class 1,

survival expectations is about 3.6 and 4.5 percentage points lower in the “smoking free

scenario” (individuals never smoked) and in the “smoking scenario” (all individuals currently

smoke). The difference between the “quitting scenario” and “smoking free scenario” is

negligible (0.6) in class 2, while survival expectations is about 3.6 percentage points lower in

17

the “smoking scenario”. Comparing the “smoking free scenario” with the “smoking scenario”

we find that expectation is higher in the first case, with a 0.9 and 2.6 percentage points

difference in class 1 and 2 respectively.

Predicted probability of SAH=1 is always lower in the “smoking free scenario”. The

highest probabilities are associated to the “quitting scenario” and the “smoking scenario”,

with a difference of about 4 and 7 percentage points with the “smoking free scenario” in class

1 and 2 respectively.

Results confirm that risk perceptions of smokers is altered by the decision to quit for what

concerns both the short and the long-term effects of smoking. Risk perception of current

smokers seems to take into account the long-term but not the short-terms effect of smoking.

5.5 Posterior analysis

Estimation shows that our two individuals types behave differently in the way they

formulate survival expectations and report subjective health. For a deeper investigation we

examine the determinants of class membership. We assign each individual to the class

associated to the larger posterior probability using a cut-off probability of 0.5 (see Atella et

al., 2004), and define a binary indicator of class membership that takes value 1 if the posterior

probability is above the cut-off probability and 0 otherwise. This is equivalent to saying that

individual i belongs to latent class 1 if the estimated posterior probability is larger than the

estimated , since

Table 10 shows that, on average, sample 1 (drawn from the first sub-population) reports a

lower probability of survival at some future age, about 59 per cent (about 70 per cent in

sample 2). In both samples about 32 per cent of respondents report very good or excellent

health, and this proportion is slightly lower in class 2 where, however, a higher percentage of

individuals reports gali limitations and a higher number of disabilities (adl and iadl). Smokers

are more concentrated in sample 2 (47.8 per cent of respondents never smoked in sample 2;

52.4 in sample 1). Of them, 21.7 per cent smoked at the time of the interview while 30.5 had

already quit (19.6 and 28 per cent in class 1); average time spent smoking is about one year

longer in the second sample. Sample 2 appears to represent a population of “more optimistic”

individuals who are also “less healthy” and “more addicted to smoking”. It is also

characterised by relatively older individuals (it includes a larger share of individuals aged 71

and over than sample 1), most of them are retired or belong to the poorest income quartiles,

have lower education and a less healthy lifestyle.

TABLE 10

18

We additionaly estimate a probit model for class membership conditional on the exogenous

variables used in the mixture model (Table 11) The probability of being assigned to class 1

(where “less optimistic”, “healthier” and “less addicted to smoking” individuals concentrate)

is significantly lower for retired, married or separated individuals, those who have been in

hospital in the last year, and have an unhealthy lifestyle. It decreases with the number of

children and increases with cognitive ability. Class membership significantly depends on age:

individuals aged 50-79 are more likely to appear in class 1, meaning that those approaching

the end of lifespan might find smoking still attractive. According to the literature, we interpret

this in terms of rational myopic behaviour: smoking is a rational choice when individuals

believe that there is not enough time left for smoking to affect mortality risk, meaning that the

associated opportunity cost is low. This finding is in line with Adda and Lechene (2001): they

present a joint model of tobacco consumption and mortality over the life-cycle where

individuals with lower life expectancy select into smoking, the cost of smoking being higher

for those with longer potential life expectancy.

TABLE 11

6 Discussion

This paper explores formation of survival expectations focusing on the role of smoking on

people's perception of health risk. The empirical literature, mainly based on US surveys,

provides mixed evidence on the relation between smoking and risk perception.

We propose a simultaneous recursive model for survival expectation, subjective health and

smoking duration. The analysis controls for endogeneity of the health and smoking variables

as well as unobservables, by means of a finite mixture model. Using data on elderly

Europeans, we provide evidence of heterogeneity in assessing survival probability and

reporting health and identify two individual types in the population, which differ in observed

characteristics as well as in the level of optimism, risk perception and rationality in addiction.

The first type does not evaluate neither the short (i.e., current health damages due to smoking)

nor the long-term effects of smoking (i.e., higher mortality risk due to smoking): in particular,

past smokers reward themselves for quitting by reporting better chances of living longer than

their smoking behaviour would warrant. For individuals of the second type, long-term effects

of smoking are neglected while short-terms effects are taken into account; current smokers do

not seem to discount future consequences on mortality risk. Furthermore, in reporting health

status, the effect of smoking duration is once again compensated by the decision to quit.

19

Particularly for older individuals, such attitudes in risk perception might depend on a lower

opportunity cost of smoking due to lower life expectancy.

Policy makers who are concerned with the prevention of health problems and the

promotion of healthy lifestyles might be interested in knowing whether and to what extent

individuals understand morbidity and mortality consequences of smoking. This paper shows

that, despite existing national anti-smoking campaigns, smokers are not necessarily fully

aware of the true health risk relative to the non-smoking population. This raises a first

question of whether more dissemination of information is needed. Reversibility of the

smoking effects reflects myopic behaviour of past smokers. This raises a second question of

whether better dissemination of information would be necessary.

Our analysis also shows that the numerical indicator of subjective survival probability is a

complete measure of survival expectations which captures observable as well as unobservable

factors influencing individual beliefs. The use of such indicator in models of health

investments over the life-cycle might be preferred to mortality hazard rates estimated from

life tables, thus giving ample scope for future research.

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8 Tables and Figures

Table 1 - Target ages in the subjective survival probability question

Age Target age Target age - Age

50-65 75 20-25

56-60 75 15-19

61-65 75 10-14

66-70 80 10-14

71-75 85 10-14

76-80 90 10-14

81-85 95 10-14

24

Table 2 - Sample means in the overall sample and by subjective survival probability

N= 20524 overall sample SSP < 50 SSP = 50 SSP > 50

subjective survival probability (SSP) 61.868 18.723 50 83.447

self-assessed health (SAH) 0.323 0.134 0.276 0.415

never smoker 0.512 0.530 0.519 0.502

current smoker 0.202 0.190 0.215 0.200

past smoker 0.286 0.279 0.266 0.298

years smoked (n=10509) 28.298 31.464 29.018 26.863

current smoker (n=4139) 36.539 39.852 36.261 35.498

past smoker (n=5876) 22.493 25.745 23.153 21.086

drinker 0.140 0.126 0.133 0.149

no physical exercise 0.083 0.170 0.079 0.053

obese 0.210 0.241 0.217 0.194

income 29185.080 23765.550 28613.970 31471.610

income 1 0.237 0.291 0.242 0.214

income 2 0.248 0.317 0.258 0.217

income 3 0.258 0.220 0.263 0.271

income 4 0.257 0.172 0.237 0.299

no education 0.046 0.063 0.045 0.040

less than Diploma 0.448 0.535 0.458 0.410

high school diploma 0.306 0.271 0.311 0.317

univeristy degree or higher 0.201 0.131 0.186 0.233

retired 0.474 0.641 0.468 0.414

employed 0.303 0.129 0.289 0.374

unemployed 0.034 0.025 0.036 0.035

sick 0.032 0.051 0.033 0.025

homemaker 0.155 0.150 0.171 0.150

married 0.750 0.661 0.738 0.789

separated or divorced 0.074 0.073 0.073 0.075

single 0.054 0.063 0.057 0.049

widowed 0.122 0.204 0.133 0.086

male 0.465 0.475 0.457 0.464

age 63.513 68.862 63.564 61.493

age 50-65 0.619 0.360 0.606 0.722

age 66-70 0.144 0.153 0.146 0.140

age 71-75 0.111 0.170 0.133 0.079

age 76-80 0.081 0.189 0.077 0.042

age 81-85 0.045 0.128 0.038 0.017

adl 1.830 2.062 1.669 1.631

iadl 1.770 2.035 1.661 1.522

gali 0.402 0.608 0.409 0.322

hospital admission in last year 0.125 0.203 0.126 0.095

tobacco related diseases 0.512 0.653 0.529 0.452

number of children 2.140 2.173 2.083 2.155

numeracy 3.400 3.124 3.424 3.492

deceased mother 0.749 0.875 0.764 0.695

age at death 74.986 74.150 74.393 75.679

deceased father 0.897 0.958 0.906 0.870

age at death 71.023 70.031 70.715 71.578

spouse age at death 63.062 66.097 62.692 60.646

northern 0.181 0.172 0.167 0.191

southern 0.272 0.237 0.278 0.281

central 0.547 0.590 0.555 0.527

25

Table 3 - Average SSP by SAH, smoking and socioeconomic status

overall distribution = 75 = 80 = 85 = 90 = 95

SAH

excellent 76.633 78.607 73.918 67.056 62.055 59.742

(0.477) (0.493) (1.548) (2.137) (3.686) (7.341)

very good 69.766 72.970 67.039 61.772 50.135 45.795

(0.357) (0.380) (1.046) (1.446) (1.964) (2.722)

good 62.786 68.004 62.352 54.567 47.284 38.819

(0.296) (0.337) (0.726) (0.890) (1.210) (1.718)

fair 51.251 58.304 53.518 47.867 37.989 29.793

(0.443) (0.592) (1.042) (1.125) (1.247) (1.528)

poor 39.166 48.076 41.652 37.734 23.629 24.058

(0.924) (1.429) (2.348) (2.146) (1.878) (2.598)

smoking status

never 61.034 68.527 61.391 53.123 42.537 33.378

(0.276) (0.316) (0.666) (0.771) (0.944) (1.244)

current 62.420 65.427 56.388 51.170 43.246 40.481

(0.437) (0.472) (1.296) (1.811) (3.120) (3.689)

past 62.969 70.291 61.841 53.205 42.047 36.345

(0.377) (0.416) (0.956) (1.137) (1.357) (1.959)

income quartile

first 58.150 64.813 59.338 53.326 43.630 38.528

(0.410) (0.521) (0.963) (1.056) (1.275) (1.775)

second 57.780 65.037 59.817 51.931 41.527 34.380

(0.414) (0.529) (0.918) (1.046) (1.326) (1.686)

third 64.265 70.199 62.781 52.508 40.901 31.213

0.380 0.405 0.986 1.257 1.620 2.363

forth 67.280 70.798 62.143 55.395 43.915 30.890

(0.365) (0.370) (1.234) (1.779) (2.243) (2.724)

education

55.983 63.446 57.207 55.418 42.014 43.898

(0.985) (1.553) (2.174) (1.941) (2.562) (3.963)

59.105 66.689 59.999 52.289 42.410 34.427

(0.309) (0.374) (0.727) (0.825) (1.005) (1.304)

63.516 68.277 62.672 51.663 41.130 34.233

(0.347) (0.379) (0.907) (1.231) (1.579) (2.111)

66.865 71.188 61.271 56.287 45.034 32.839

(0.400) (0.410) (1.245) (1.633) (2.144) (3.143)

SSP

less than diploma

no education

high school diploma

university degree or

higher

The table reports average SSP by SAH category, smoking status, income quartile and educational level.

Averages are calculated for the overall sample , that is considering all target ages, and for each specific

target age.

26

Table 4 - Distributions of self-assessed health and smoking variables

first second third fourth excellent very good good fair poor

SAH

excellent 0.054 0.090 0.134 0.186

(0.002) (0.008) (0.005) (0.005)

very good 0.158 0.211 0.276 0.263

(0.004) (0.012) (0.006) (0.006)

good 0.396 0.462 0.406 0.387

(0.005) (0.014) (0.007) (0.007)

fair 0.295 0.206 0.158 0.135

(0.005) (0.012) (0.005) (0.005)

poor 0.097 0.030 0.026 0.030

(0.003) (0.005) (0.002) (0.002)

smoking status

never 0.524 0.531 0.515 0.482 0.471 0.492 0.513 0.550 0.515

(0.005) (0.014) (0.007) (0.007) (0.011) (0.008) (0.006) (0.007) (0.014)

current 0.204 0.199 0.192 0.207 0.201 0.221 0.202 0.183 0.198

(0.004) (0.012) (0.006) (0.006) (0.009) (0.006) (0.004) (0.006) (0.011)

past 0.272 0.269 0.293 0.311 0.328 0.287 0.285 0.266 0.288

(0.005) (0.013) (0.006) (0.007) (0.010) (0.007) (0.005) (0.007) (0.013)

years smoked

current smoker 37.759 36.899 35.064 35.578 35.166 34.880 36.782 37.948 39.332

(0.285) (0.657) (0.361) (0.354) (0.534) (0.366) (0.283) (0.441) (0.817)

past smoker 24.344 22.803 20.591 21.198 18.678 20.462 21.886 26.320 28.806

(0.279) (0.717) (0.335) (0.319) (0.449) (0.355) (0.268) (0.404) (0.768)

SSP quartile SAH

The “SSP quartile” panel describes the distributions of SAH and smoking status by SSP quartile and the average number of years

smoked in each quartile; the “SAH” panel describes the distribution of smoking status and the average number of years smoked by

SAH category.

27

Table 5 – Average SSP by target age and parental/spouse mortality

SSP SSP SSP

overall

distribution= 75 = 80 = 85 = 90 = 95

overall

distribution= 75 = 80 = 85 = 90 = 95

overall

distribution= 75 = 80 = 85 = 90 = 95

dead 59.235 67.182 60.161 52.717 42.453 34.825 60.815 67.677 60.638 52.886 42.426 34.841 51.281 65.750 58.126 53.448 39.432 33.731

(0.236) (0.290) (0.525) (0.610) (0.754) (1.015) (0.212) (0.247) (0.509) (0.602) (0.754) (1.014) (0.607) (1.009) (1.343) (1.246) (1.317) (1.424)

alive 69.727 69.916 68.113 61.698 30.000 - 71.056 71.082 69.048 97.500 - - 63.337 68.368 61.174 52.782 43.787 35.776

(0.339) (0.346) (1.745) (3.481) (25.166) - (0.509) (0.516) (3.171) (2.500) - - (0.207) (0.229) (0.544) (0.687) (0.916) (1.432)

age at death

< =50 56.159 65.035 58.494 51.957 38.241 34.988 60.086 67.694 59.194 51.879 44.402 36.821 60.736 67.781 61.618 52.941 35.971 41.923

(0.937) (1.223) (2.198) (2.325) (2.525) (3.366) (0.694) (0.864) (1.475) (1.837) (2.425) (3.424) (1.375) (1.656) (3.377) (3.894) (4.529) (4.403)

51 - 74 57.882 64.888 56.304 50.512 40.912 35.609 59.202 65.351 58.183 50.731 42.107 32.107 51.392 64.767 56.716 52.729 39.488 33.159

(0.409) (0.484) (1.008) (1.183) (1.379) (1.847) (0.321) (0.373) (0.813) (0.951) (1.194) (1.473) (0.745) (1.289) (1.508) (1.420) (1.760) (1.994)

75 - 79 59.623 67.639 57.589 50.680 42.417 30.945 61.471 68.966 60.678 52.219 40.635 38.542 42.652 70.000 67.500 59.595 37.316 32.022

(0.586) (0.672) (1.436) (1.584) (2.107) (2.621) (0.523) (0.593) (1.313) (1.505) (1.752) (2.621) (1.913) (7.508) (5.846) (4.251) (2.749) (3.123)

80 - 84 60.542 69.360 61.904 51.817 41.142 32.583 62.509 70.442 62.501 52.716 41.414 35.949 41.250 26.667 53.750 63.846 42.510 34.714

(0.533) (0.643) (1.158) (1.322) (1.704) (2.433) (0.533) (0.586) (1.301) (1.522) (1.812) (2.837) (2.558) (12.019) (12.947) (6.557) (4.042) (3.700)

85 - 89 60.112 69.287 63.893 54.191 41.248 27.797 63.265 71.330 64.820 56.152 40.725 33.948 46.744 - - 43.333 53.308 36.471

(0.629) (0.803) (1.175) (1.567) (1.906) (2.622) (0.689) (0.770) (1.533) (1.864) (2.554) (3.150) (5.384) - - (11.450) (8.729) (8.366)

older than 90 61.255 70.441 64.121 58.427 51.049 44.116 64.216 70.960 66.538 63.659 50.752 38.653 31.333 35.000 28.889

(0.707) (1.073) (1.358) (1.526) (1.995) (2.542) (0.880) (1.142) (1.754) (2.057) (2.974) (3.803) (7.096) (8.851) (10.599)

mother father partner/spouse

28

Table 6 - Information criteria, one class and two class model

Single class model Mixture model

-2logL 67602.406 54119.866

AIC 67812.406 54330.866

CAIC 68645.988 56215.959

BIC 68644.988 56214.959

no. parameters 105 211

N 20524 20524

The consistent Akaike information criterion (CAIC) is calculated as

2logL+[1+log

(N)q] where q is the number of parameters.

29

Table 7 - Estimated coefficients from the finite mixture model

variables

sah 0.319 (0.014) *** 0.430 (0.035) ***

current smoker -0.039 (0.124) -0.121 (0.261) 0.148 (0.237) 0.264 (0.287)

past smoker 0.153 (0.050) *** 0.027 (0.120) 0.148 (0.095) 0.277 (0.133) *

ln(years smoked)*current smoker -0.016 (0.034) 0.013 (0.072) -0.061 (0.066) -0.104 (0.080)

ln(years smoked)*past smoker -0.039 (0.016) ** 0.008 (0.039) -0.055 (0.032) -0.106 (0.044) *

income 2 -0.032 (0.019) * -0.024 (0.046) 0.048 (0.038) -0.088 (0.054) -0.082 (0.038) * -0.085 (0.047) 0.129 (0.034) *** 0.081 (0.045)

income 3 0.030 (0.020) 0.122 (0.048) ** 0.009 (0.040) 0.103 (0.056) -0.165 (0.038) *** -0.136 (0.049) ** 0.186 (0.035) *** 0.081 (0.048)

income 4 0.059 (0.021) ** 0.041 (0.052) 0.099 (0.042) * 0.183 (0.059) ** -0.182 (0.041) *** -0.141 (0.051) ** 0.142 (0.037) *** 0.118 (0.050) *

less than Diploma -0.085 (0.032) ** 0.059 (0.078) 0.259 (0.077) *** 0.284 (0.106) ** 0.167 (0.068) * 0.219 (0.080) ** 0.252 (0.060) *** 0.171 (0.077) *

high school diploma -0.056 (0.034) 0.117 (0.082) 0.420 (0.078) *** 0.409 (0.108) *** 0.158 (0.070) * 0.201 (0.083) * 0.248 (0.062) *** 0.224 (0.081) **

univeristy degree or higher 0.018 (0.036) 0.068 (0.088) 0.653 (0.080) *** 0.537 (0.112) *** 0.020 (0.071) 0.029 (0.086) 0.209 (0.065) ** 0.157 (0.085)

retired 0.019 (0.019) 0.086 (0.047) * -0.034 (0.038) 0.047 (0.055) -0.109 (0.041) ** -0.017 (0.052)

employed 0.097 (0.021) *** 0.235 (0.051) *** 0.203 (0.039) *** 0.233 (0.056) *** -0.188 (0.040) *** -0.055 (0.053)

male -0.087 (0.015) *** -0.115 (0.036) *** 0.022 (0.028) 0.051 (0.040) 0.008 (0.027) 0.053 (0.035) 0.833 (0.023) *** 0.820 (0.032) ***

age 50-65 0.908 (0.037) *** 1.461 (0.080) *** 0.205 (0.084) * 0.357 (0.106) *** 0.006 (0.067) 0.187 (0.074) * 0.382 (0.062) *** 0.421 (0.071) ***

age 66-70 0.752 (0.038) *** 1.165 (0.082) *** 0.113 (0.086) 0.229 (0.109) 0.031 (0.068) 0.068 (0.076) 0.154 (0.067) * 0.115 (0.079)

age 71-75 0.498 (0.038) *** 0.884 (0.084) *** 0.022 (0.088) 0.077 (0.113) -0.024 (0.069) 0.069 (0.077) 0.072 (0.069) 0.153 (0.082)

age 76-80 0.195 (0.040) *** 0.333 (0.085) *** 0.014 (0.094) -0.104 (0.120) -0.151 (0.072) * 0.027 (0.078) 0.002 (0.073) 0.072 (0.084)

married 0.066 (0.028) ** 0.342 (0.075) *** 0.010 (0.054) 0.303 (0.088) *** -0.172 (0.058) ** -0.232 (0.079) *

separated or divorced 0.071 (0.035) * 0.084 (0.092) -0.084 (0.069) 0.470 (0.106) *** 0.057 (0.071) 0.081 (0.096)

widowed -0.064 (0.053) 0.235 (0.130) * -0.031 (0.067) 0.360 (0.104) *** -0.011 (0.071) -0.040 (0.094)

target age - age -0.015 (0.002) *** -0.024 (0.005) ***

partner age at death < 50 0.073 (0.063) 0.119 (0.156)

partner age at death 51-74 0.029 (0.050) -0.073 (0.118)

mother died -0.100 (0.019) *** -0.054 (0.046)

mother age at death < 50 -0.012 (0.030) -0.113 (0.072)

mother age at death 75-79 0.007 (0.021) -0.071 (0.053)

mother age at death 80-84 0.038 (0.020) * 0.001 (0.049)

mother age at death 85-89 0.040 (0.022) * -0.005 (0.054)

father died -0.141 (0.024) *** -0.139 (0.058) ***

father age at death < 50 0.038 (0.024) 0.048 (0.057)

father age at death 75-79 0.085 (0.019) *** 0.012 (0.047)

father age at death 80-84 0.108 (0.019) *** 0.089 (0.048) *

father age at death 85-89 0.161 (0.024) *** 0.058 (0.058)

numeracy 0.002 (0.007) 0.050 (0.016) ***

adl -0.155 (0.048) ** -0.516 (0.095) ***

iadl -0.176 (0.035) *** -0.261 (0.052) ***

gali -1.049 (0.030) *** -0.986 (0.042) ***

hospital admission in last year -0.246 (0.045) *** -0.299 (0.063) ***

drinker 0.132 (0.030) *** 0.100 (0.039) *

no physical exercise 0.265 (0.054) *** 0.286 (0.058) ***

obese -0.107 (0.029) *** -0.127 (0.037) ***

tobacco-related diseases -0.128 (0.024) *** -0.039 (0.031)

number of children -0.006 (0.009) 0.046 (0.011)

northern -0.132 (0.022) *** -0.263 (0.050) *** 0.636 (0.041) *** 0.707 (0.056) *** -0.096 (0.039) * -0.123 (0.048) * 0.280 (0.037) *** 0.465 (0.049) ***

central -0.106 (0.016) *** -0.330 (0.040) *** 0.011 (0.032) 0.111 (0.045) * -0.164 (0.032) *** -0.165 (0.041) *** 0.079 (0.029) ** 0.134 (0.039) ***

intercept -0.059 (0.071) -0.542 (0.171) -0.820 (0.124) *** -1.343 (0.173) *** 4.181 (0.114) *** 3.764 (0.140) *** -1.174 (0.084) *** -1.046 (0.102) ***

f 6.735 (0.077) 0.421 (0.006) 1.422 (0.021) *** 1.454 (0.028) ***

N 20524 logL

Standard errors in parenthesis. Level of significance: *** 1%; ** 5%; * 10%.

-27059.933

class 1 class2 class2class 1

probability of starting survival expectations subjective health smoking duration

class2 class2class 1 class 1

30

Table 8 - Estimated odds ratios for SSP and average partial effects for SAH

variables class 1 class2 class 1 class2

sah 1.376 1.537

current smoker 0.962 0.886 0.042 0.074

past smoker 1.166 1.028 0.042 0.077

ln(years smoked)*current smoker 0.984 1.013 -0.018 -0.028

ln(years smoked)*past smoker 0.962 1.008 -0.016 -0.029

income 2 0.969 0.977 0.014 -0.024

income 3 1.030 1.130 0.003 0.029

income 4 1.060 1.042 0.028 0.053

less than Diploma 0.919 1.061 0.068 0.074

high school diploma 0.946 1.125 0.114 0.109

univeristy degree or higher 1.018 1.070 0.185 0.147

retired 1.020 1.089 -0.010 0.013

employed 1.101 1.265 0.060 0.067

male 0.916 0.892 0.006 0.014

age 50-65 2.479 4.312 0.058 0.099

age 66-70 2.121 3.207 0.031 0.062

age 71-75 1.646 2.420 0.006 0.020

age 76-80 1.215 1.396 0.004 -0.026

married 1.068 1.407 0.003 0.080

separated or divorced 1.074 1.088 -0.024 0.128

widowed 0.938 1.265 -0.009 0.097

target age - age 0.985 0.976

partner age at death < 50 1.076 1.127

partner age at death 51-74 1.029 0.930

mother died 0.905 0.948

mother age at death < 50 0.988 0.893

mother age at death 75-79 1.008 0.931

mother age at death 80-84 1.039 1.001

mother age at death 85-89 1.040 0.995

father died 0.869 0.870

father age at death < 50 1.039 1.049

father age at death 75-79 1.089 1.012

father age at death 80-84 1.115 1.093

father age at death 85-89 1.175 1.060

numeracy 1.002 1.051

adl -0.045 -0.137

iadl -0.051 -0.071

gali -0.300 -0.276

hospital admission in last year -0.068 -0.081

drinker

no physical exercise

obese

tobacco-related diseases

number of children

northern 0.877 0.769 0.193 0.208

central 0.900 0.719 0.003 0.031

baseline individual 0.754 0.475

survival expectation subjective health

31

Table 9 - Predicted average SSP and average probability of SAH=1 for hypothetical scenarios and by

target age

class 1 class 2 class 1 class 2 class 1 class 2 class 1 class 2 class 1 class 2 class 1 class 2

Predicted average SSP

observed smoking bahaviour 0.581 0.652 0.622 0.713 0.585 0.650 0.523 0.585 0.448 0.452 0.401 0.373

smoking scenario 0.564 0.630 0.604 0.691 0.567 0.626 0.505 0.560 0.430 0.426 0.384 0.349

quitting scenario 0.609 0.661 0.649 0.721 0.613 0.660 0.552 0.595 0.477 0.462 0.429 0.383

smoking free scenario 0.573 0.656 0.614 0.716 0.576 0.654 0.514 0.589 0.440 0.456 0.393 0.377

Predicted average probability of SAH=1

observed smoking bahaviour 0.322 0.326 0.336 0.349 0.309 0.312 0.284 0.270 0.282 0.224 0.278 0.250

smoking scenario 0.343 0.362 0.358 0.387 0.331 0.349 0.305 0.306 0.302 0.257 0.298 0.285

quitting scenario 0.344 0.366 0.358 0.391 0.331 0.353 0.305 0.309 0.303 0.261 0.299 0.288

smoking free scenario 0.301 0.289 0.315 0.311 0.289 0.275 0.264 0.236 0.262 0.194 0.258 0.217

SSP

= 95overall = 75 = 80 = 85 = 90

32

Table 10 – Sample means in the heterogenous population

variables sample 1 sample 2

N=15093 N=5431

subjective survival probability (SSP) 58.974 69.908

self-assessed health (SAH) 0.324 0.321

never smoker 0.524 0.478

current smoker 0.196 0.217

past smoker 0.280 0.305

years smoked (n=10509) 28.062 28.897

current smoker (n=4139) 36.295 37.150

past smoker (n=5876) 22.290 23.013

drinker 0.138 0.147

no physical exercise 0.071 0.119

obese 0.206 0.220

income 1 0.234 0.245

income 2 0.242 0.262

income 3 0.263 0.247

income 4 0.261 0.246

no education 0.045 0.048

less than Diploma 0.437 0.476

high school diploma 0.309 0.298

univeristy degree or higher 0.209 0.178

retired 0.463 0.504

employed 0.310 0.284

unemployed 0.035 0.031

sick 0.029 0.040

homemaker 0.161 0.138

married 0.749 0.753

separated or divorced 0.074 0.074

single 0.057 0.045

widowed 0.120 0.127

male 0.463 0.469

age 63.234 64.289

age 50-65 0.628 0.594

age 66-70 0.148 0.133

age 71-75 0.109 0.116

age 76-80 0.076 0.096

age 81-85 0.039 0.061

adl 0.128 0.200

iadl 0.217 0.323

gali 0.395 0.423

tobacco related diseases 0.509 0.520

hospital admission in last year 0.119 0.140

number of children 2.112 2.220

numeracy 3.440 3.288

deceased mother 0.744 0.763

age at death 74.993 74.967

deceased father 0.895 0.905

age at death 71.114 70.772

spouse age at death 62.794 63.766

northern 0.168 0.218

southern 0.269 0.279

central 0.563 0.502

33

Table 11 - Probit model for class membership, standard errors in brackets

variables

income 2 -0.029 (0.028)

income 3 0.034 (0.030)

income 4 0.004 (0.032)

less than Diploma -0.069 (0.047)

high school diploma -0.063 (0.051)

univeristy degree or higher -0.004 (0.054)

retired -0.088 (0.029)

employed -0.042 (0.032)

male -0.021 (0.021)

age 50-65 0.163 (0.052)

age 66-70 0.269 (0.053)

age 71-75 0.184 (0.053)

age 76-80 0.105 (0.054)

married -0.122 (0.046)

separated or divorced -0.115 (0.056)

widowed 0.002 (0.081)

target age - age 0.002 (0.003)

partner age at death < 50 -0.002 (0.095)

partner age at death 51-74 -0.096 (0.073)

mother died 0.001 (0.028)

mother age at death < 50 -0.008 (0.045)

mother age at death 75-79 0.023 (0.032)

mother age at death 80-84 0.013 (0.030)

mother age at death 85-89 -0.017 (0.033)

father died -0.008 (0.036)

father age at death < 50 -0.051 (0.035)

father age at death 75-79 -0.003 (0.029)

father age at death 80-84 0.029 (0.029)

father age at death 85-89 0.001 (0.036)

numeracy 0.057 (0.010)

adl -0.024 (0.019)

iadl -0.020 (0.016)

gali 0.028 (0.021)

hospital admission in last year -0.060 (0.029)

drinker -0.078 (0.028)

no physical exercise -0.270 (0.037)

obese -0.034 (0.024)

tobacco-related diseases 0.023 (0.020)

number of children -0.020 (0.007)

northern -0.199 (0.031)

central 0.049 (0.024)

intercept 0.564 (0.109)

Probability of class membership

34

Figure 1 – Distribution of SSP, average SSP and Life Tables probability by target age and European regions

010

20

30

010

20

30

010

20

30

010

20

30

010

20

30

0 50 100 0 50 100 0 50 100

SSP = 72; Life Tables = 78.6 SSP = 66.9; Life Tables = 76.5 SSP = 68.4; Life Tables = 80.2

SSP = 61.8; Life Tables = 70.9 SSP = 58.9; Life Tables = 68.5 SSP = 63.6; Life Tables = 72.4

SSP = 52.4; Life Tables = 53.9 SSP = 50.4; Life Tables = 52.1 SSP = 52.8; Life Tables = 56.1

SSP = 41.5; Life Tables = 32.0 SSP = 39.3; Life Tables = 31.7 SSP = 49.7; Life Tables = 30.1

SSP = 31.8; Life Tables = 13.0 SSP = 31.8; Life Tables = 13.7 SSP = 44.5; Life Tables = 16.3

Northern Central Southern

T=75

T=80

T=85

T=90

T=95